Understanding the Physics

* Gravity: The ball accelerates downwards due to gravity, which has an acceleration of approximately 9.8 m/s².

* Free Fall: Since the ball is dropped from rest, we're dealing with free fall motion.

Formulas

We'll use the following kinematic equation to find the distance traveled:

* d = v₀t + (1/2)at²

Where:

* d = distance traveled

* v₀ = initial velocity (0 m/s since the ball is dropped from rest)

* t = time (10 seconds)

* a = acceleration due to gravity (9.8 m/s²)

Calculation

1. Plug in the values:

d = (0 m/s)(10 s) + (1/2)(9.8 m/s²)(10 s)²

2. Simplify:

d = 0 + (4.9 m/s²)(100 s²)

3. Calculate:

d = 490 meters

Answer: The ball will have traveled approximately 490 meters after 10 seconds.